In trade, weights and measures is often a subject of governmental regulation, to ensure fairness and transparency. The Bureau international des poids et mesures (BIPM) is tasked with ensuring worldwide uniformity of measurements and their traceability to the International System of Units (SI). Metrology is the science for developing national and internationally accepted units of weights and measures.

A unit of measurement is a standardised quantity of a physical property, used as a factor to express occurring quantities of that property. Units of measurement were among the earliest tools invented by humans. Primitive societies needed rudimentary measures for many tasks: constructing dwellings of an appropriate size and shape, fashioning clothing, or bartering food or raw materials.

සැකිල්ල:Vitruvian Man Measurements Prior to the near global adoption of the metric system many different systems of measurement had been in use. Many of these were related to some extent or other. Often they were based on the dimensions of the human body according to the proportions described by Marcus Vitruvius Pollio. As a result, units of measure could vary not only from location to location, but from person to person.

Both the Imperial units and US customary units derive from earlier English units. Imperial units were mostly used in the British Commonwealth and the former බ්‍රිතාන්‍ය අධිරාජ්‍යය. US customary units are still the main system of measurement used in the United States despite Congress having legally authorized metric measure on 28 July 1866.[1] Some steps towards US metrication have been made, particularly the redefinition of basic US units to derive exactly from SI units, so that in the US the inch is now defined as 0.0254 m (exactly), and the avoirdupois pound is now defined as 453.59237 g (exactly)[2]

While the above systems of units are based on arbitrary unit values, formalised as standards, some unit values occur naturally in science. Systems of units based on these are called natural units. Similar to natural units, atomic units (au) are a convenient system of units of measurement used in atomic physics.

Different systems of units are based on different choices of a set of fundamental units. The most widely used system of units is the International System of Units, or SI. There are seven SI base units. All other SI units can be derived from these base units.

For most quantities a unit is absolutely necessary to communicate values of that physical quantity. For example, conveying to someone a particular length without using some sort of unit is impossible, because a length cannot be described without a reference used to make sense of the value given.

But not all quantities require a unit of their own. Using physical laws, units of quantities can be expressed as combinations of units of other quantities. Thus only a small set of units is required. These units are taken as the base units. Other units are derived units. Derived units are a matter of convenience, as they can be expressed in terms of basic units. Which units are considered base units is a matter of choice.

The base units of SI are actually not the smallest set possible. Smaller sets have been defined. For example, there are unit sets in which the electric and magnetic field have the same unit. This is based on physical laws that show that electric and magnetic field are actually different manifestations of the same phenomenon.

Any value of a physical quantity is expressed as a comparison to a unit of that quantity. For example, the value of a physical quantity Z is written as the product of a unit [Z] and a numerical factor:

Z=n×[Z]=n[Z].{\displaystyle Z=n\times [Z]=n[Z].}

The multiplication sign is usually left out, just as it is left out between variables in scientific notation of formulas. In formulas the unit [Z] can be treated as if it were a kind of physical dimension: see dimensional analysis for more on this treatment.

A distinction should be made between units and standards. A unit is fixed by its definition, and is independent of physical conditions such as temperature. By contrast, a standard is a physical realization of a unit, and realizes that unit only under certain physical conditions. For example, the metre is a unit, while a metal bar is a standard. One metre is the same length regardless of temperature, but a metal bar will be one metre long only at a certain temperature.

Treat units algebraically. Only add like terms. When a unit is divided by itself, the division yields a unitless one. When two different units are multiplied, the result is a new unit, referred to by the combination of the units. For instance, in SI, the unit of speed is metres per second (m/s). See dimensional analysis. A unit can be multiplied by itself, creating a unit with an exponent (e.g. m²/s²).

Some units have special names, however these should be treated like their equivalents. For example, one newton (N) is equivalent to one kg•m/s². This creates the possibility for units with multiple designations, for example: the unit for surface tension can be referred to as either N/m (newtons per metre) or kg/s² (kilograms per second squared).

Conversion of units involves comparison of different standard physical values, either of a single physical quantity or of a physical quantity and a combination of other physical quantities.

Starting with:

Z=ni×[Z]i{\displaystyle Z=n_{i}\times [Z]_{i}}

just replace the original unit [Z]i{\displaystyle [Z]_{i}} with its meaning in terms of the desired unit [Z]j{\displaystyle [Z]_{j}}, e.g. if [Z]i=cij×[Z]j{\displaystyle [Z]_{i}=c_{ij}\times [Z]_{j}}, then:

For example, you have an expression for a physical value Z involving the unit feet per second ([Z]i{\displaystyle [Z]_{i}}) and you want it in terms of the unit miles per hour ([Z]j{\displaystyle [Z]_{j}}):

Find facts relating the original unit to the desired unit:

1 mile = 5280 feet and 1 hour = 3600 seconds

Next use the above equations to construct a fraction that has a value of unity and that contains units such that, when it is multiplied with the original physical value, will cancel the original units:

Last,multiply the original expression of the physical value by the fraction, called a conversion factor, to obtain the same physical value expressed in terms of a different unit. Note: since valid conversion factors are dimensionless and have a numerical value of one, multiplying any physical quantity by such a conversion factor (which is 1) does not change that physical quantity.

One example of the importance of agreed units is the failure of the NASAMars Climate Orbiter, which was accidentally destroyed on a mission to the planetMars in September 1999 instead of entering orbit, due to miscommunications about the value of forces: different computer programs used different units of measurement (newton versus pound force). Enormous amounts of effort, time, and money were wasted.[3][4]

On April 151999Korean Air cargo flight 6316 from Shanghai to Seoul was lost due to the crew confusing tower instructions (in metres) and altimeter readings (in feet). Three crew and five people on the ground were killed. Thirty seven were injured.[5][6]

In 1983, a Boeing 767 (which came to be know as the Gimli Glider) ran out of fuel in mid-flight because of two mistakes in figuring the fuel supply of Air Canada's first aircraft to use metric measurements.[7] This accident is apparently the result of confusion both due to the simultaneous use of metric & Imperial measures as well as mass & volume measures.

↑"Jet's Fuel Ran Out After Metric Conversion Errors". New York Times. July 30, 1983. සම්ප්‍රවේශය 2007-08-21. Air Canada said yesterday that its Boeing 767 jet ran out of fuel in mid-flight last week because of two mistakes in figuring the fuel supply of the airline's first aircraft to use metric measurements. After both engines lost their power, the pilots made what is now thought to be the first successful emergency dead stick landing of a commercial jetliner.